Abstract
A key aspect in understanding patterns in wood demand and harvesting activities is monitoring of timber products output by wood processing facilities. Estimation of change from year-to-year is necessary but is complicated due to shifts in the population as well as changing strata over time. Taking independent samples each year eases complexity, yet suffers from relatively large sampling error in comparison to other designs that take advantage of the covariance arising from correlated samples. In this study, a design intended to maximize the precision of the change estimate by retaining the initial sample to the extent possible was analyzed. Several approaches to estimating the covariance, with the primary challenge being that sometimes only a single sample unit occurred in both samples within a given stratum. Variance underestimation and overestimation were encountered depending on the covariance method. The best outcome was attained using a measure-of-size variable at the population level to approximate the covariance. However, this approach overestimated the variance by 11% in a Monte Carlo simulation. The simulation results suggested a 14% reduction in the standard error of the estimate was attainable from correlated samples relative to independent samples. Due to the challenges introduced for estimating the covariance for changing populations and strata over time, the value of relatively small reductions in sampling error need to be considered in the context of introducing complex and potentially unreliable covariance estimation methods.
Similar content being viewed by others
References
Alberdi I, Michalak R, Fischer C, Gasparini P, Brändli UB, Tomter SM, Kuliesis A, Snorrason A, Redmond J, Hernández L, Lanz A (2016) Towards harmonized assessment of European forest availability for wood supply in Europe. Forest Policy Econ 70:20–29
Angers VA, Messier C, Beaudet M, Leduc A (2005) Comparing composition and structure in old-growth and harvested (selection and diameter-limit cuts) northern hardwood stands in Quebec. For Ecol Manag 217(2–3):275–293
Bentley JW, Johnson TG (2011) Mississippi’s timber industry—an assessment of timber product output and use, 2009. Resource bulletin SRS-181. USDA Forest Service, Southern Research Station, Asheville
Berger YG (2004) Variance estimation for measures of change in probability sampling. Can J Stat 32(4):451–467
Brandeis C, Hodges DG (2015) Forest sector and primary forest products industry contributions to the economies of the southern states: 2011 update. J Forest 113(2):205–209
Chaudhary A, Burivalova Z, Koh LP, Hellweg S (2016) Impact of forest management on species richness: global meta-analysis and economic trade-offs. Sci Rep 6:23954. https://doi.org/10.1038/srep23954
Chen W, Xu D, Liu J (2015) The forest resources input–output model: an application in China. Ecol Ind 51:87–97
Coulston JW, Westfall JA, Wear DN, Edgar CB, Prisley SP, Treiman TB, Abt RC, Smith WB (2018) Annual monitoring of U.S. timber production: rationale and design. Forest Sci 64(5):533–543
Crow TR, Buckley DS, Nauertz EA, Zasada JC (2002) Effects of management on the composition and structure of northern hardwood forests in Upper Michigan. Forest Sci 48(1):129–145
du Toit B, Malherbe GF, Lambrechts H, Naidoo S, Eatwell K (2018) Market analysis to assess timber products from dryland woodlots and farm forests in South Africa. In: Revermann R, Krewenka KM, Schmiedel U, Olwoch JM, Helmschrot J, Jürgens N (eds) Climate change and adaptive land management in southern Africa—assessments, changes, challenges, and solutions. Klaus Hess Publishers, Göttingen and Windhoek
Efron B (1979) Bootstrap methods: another look at the Jackknife. Ann Stat 7:1–26
Gregoire TG, Valentine HT (2008) Sampling strategies for natural resources and the environment. Chapman and Hall/CRC, Boca Raton
Hall JS, Harris DJ, Medjibe V, Ashton PMS (2003) The effects of selective logging on forest structure and tree species composition in a Central African forest: implications for management of conservation areas. For Ecol Manag 183(1–3):249–264
Hidiroglou MG, Särndal C-E, Binder D (1995) Weighting and estimation in business surveys. In: Cox BG, Binder DA, Chinnappa BN, Christianson A, Colledge M, Kott PS (eds) Business survey methods. Wiley, New York
Howard JL, McKeever DB (2016) U.S. forest products annual market review and prospects, 2012–2016. Research note FPL–RN–0343. USDA Forest Service Forest Products Laboratory, Madison
Howard JL, Westby R (2009) U.S. forest products annual market review and prospects, 2005–2009. Research note FPL-RN-0313. USDA Forest Service, Forest Products Laboratory, Madison
Johnson TG, Bentley JW, Howell M (2011) The South’s timber industry—an assessment of timber product output and use, 2009. Resource Bulletin SRS–182. USDA Forest Service, Southern Research Station, Asheville
Knottnerus P, van Delden A (2012) On variances of changes estimated from rotating panels and dynamic strata. Surv Methodol 38(1):43–52
Luppold W, Pugh S (2016) Diversity of the eastern hardwood resource and how this diversity influences timber utilization. For Prod J 66(1):58–65
Nanang DM (2010) Analysis of export demand for Ghana’s timber products: a multivariate co-integration approach. J for Econ 16(1):47–61
Nordberg L (2000) On variance estimation for measures of change when samples are coordinated by the use of permanent random numbers. J off Stat 16(4):363–378
O’Brien M, Bringezu S (2018) European timber consumption: developing a method to account for timber flows and the EU’s global forest footprint. Ecol Econ 147:322–332
Pepke E (2010) Forest products annual market review 2009–2010 (No. 25). United Nations Publications, Geneva
Rubilar RA, Allen HL, Fox TR, Cook RL, Albaugh TJ, Campoe OC (2018) Advances in silviculture of intensively managed plantations. Curr for Rep 4(1):23–34
Schreuder HT, Li J, Scott CT (1993) Estimation with different stratification at two occasions. Forest Sci 39(2):368–382
Schreuder HT, Ernst R, Ramirez-Maldonado H (2004) Statistical techniques for sampling and monitoring natural resources. General technical reports. RMRS-GTR-126. USDA Forest Service, Rocky Mountain Research Station, Fort Collins
Scott CT (1986) An evaluation of sampling with partial replacement. Use of auxiliary information in natural resource inventories. Use of auxiliary information in natural resource inventories. Society of American Foresters, Maryland, pp 74–79
Singh B, Sedransk J (1988) Variance estimation in stratified sampling when strata sample sizes are small. Sankhyā Indian J Stat Ser B (1960–2002) 50(3):382–393
Tukey JW (1958) Bias and confidence in not-quite large samples. Ann Math Statist 29:614
Tukey JW (1977) Exploratory data analysis. Addison-Wesley series in behavioral science: quantitative methods. Addison-Wesley, Reading
Wear DN, Prestemon JP, Foster MO (2016) US forest products in the global economy. J for 114(4):483–493
Wood J (2008) On the covariance between related Horvitz-Thompson estimators. J off Stat 24(1):53–78
Woodall CW, Ince PJ, Skog KE, Aguilar FX, Keegan CE, Sorenson CB, Hodges DG, Smith WB (2012) An overview of the forest products sector downturn in the United States. For Prod J 61:595–603
Acknowledgements
The authors are grateful to the editor and 2 anonymous reviewers for providing insightful comments that improved the manuscript.
Author information
Authors and Affiliations
Corresponding author
Additional information
Handling Editor: Pierre Dutilleul.
Rights and permissions
About this article
Cite this article
Westfall, J.A., Coulston, J.W. Estimating change in annual timber products output using a stratified sampling with certainty design. Environ Ecol Stat 29, 415–431 (2022). https://doi.org/10.1007/s10651-022-00533-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10651-022-00533-8